Bayesian Modeling and Estimation of Spatial Risk for Hospitalization and Mortality from Ischemic Heart Disease in Paraná, Brazil

Objective: Despite significant advancements in understanding risk factors and treatment strategies, ischemic heart disease (IHD) remains the leading cause of mortality worldwide, particularly within specific regions in Brazil, where the disease is a burden. Therefore, the aim of this study was to estimate the risk of hospitalization and mortality from IHD in the state of Paraná (Brazil), using spatial analysis to identify areas with higher risk based on socioeconomic, demographic and health variables. Methods: This is an ecological study based on secondary and retrospective IHD hospitalization and mortality data obtained from the Brazilian Hospitalization and Mortality Information Systems during the 2010–2021 period. Data were analyzed for 399 municipalities and 22 health regions in the state of Paraná. To assess the spatial patterns of the disease and identify relative risk (RR) areas, we constructed a risk model by Bayesian inference using the R-INLA and SpatialEpi packages in R software. Results: A total of 333,229 hospitalizations and 73,221 deaths occurred in the analyzed period, and elevated RR of hospitalization (RR = 27.412, CI 21.801; 34.466) and mortality (RR = 15.673, CI 2.148; 114.319) from IHD occurred in small-sized municipalities. In addition, medium-sized municipalities also presented elevated RR of hospitalization (RR = 6.533, CI 1.748; 2.006) and mortality (RR = 6.092, CI 1.451; 2.163) from IHD. Hospitalization and mortality rates were higher in white men aged 40–59 years. A negative association was found between Municipal Performance Index (IPDM) and IHD hospitalization and mortality. Conclusion: Areas with increased risk of hospitalization and mortality from IHD were found in small and medium-sized municipalities in the state of Paraná, Brazil. These results suggest a deficit in health care attention for IHD cases in these areas, potentially due to a low distribution of health care resources.


Observed Cases
We obtain the number of cases for all strata combined in each municipality and year by aggregating the data by municipality.To do this, we use the aggregate() function specifying the cases vector, the list of grouping elements such as list(county = data$name, year = data$year), and the function to be applied to subsets of data, which is the mean.We also set the names of the returned data frame as county, year, and Y.
These random effects capture spatial variation or unexplained variation beyond the overall intercept.
They reflect the unique characteristics of each unit of analysis.
β: Represents the overall effect of the time variable (tj) on the occurrence rate.It is a parameter that models the average temporal trend across all contexts.
δi: Represents the specific effect of each municipality for the time variable (tj).These effects capture the specific temporal variation of each unit of analysis.tj: Is the time variable that may represent different time points at which data were collected.It is used to model temporal variations in the occurrence rate.
Poisson: Refers to the Poisson distribution, which is a discrete probability distribution used to model the number of rare or discrete events occurring in a fixed time or space interval.In this context, we assume that the number of observed cases follows a Poisson distribution.nij: Represents the number of people or the population at risk in the same context where we are counting the cases.In other words, it is the number of individuals who are potentially subject to the event we are studying.Θij: Is the parameter of the Poisson distribution and represents the rate of occurrence of the event in question in the specific context (municipality, year.).It is the value we are trying to estimate or model.Therefore, the formula "Oij ~ Poisson (nijΘij)" indicates that we are modeling the number of observed cases (Oij) as a random variable following a Poisson distribution, where the rate of occurrence (Θij) is multiplied by the population at risk (nij) to determine the probability of observing a specific number of cases.log(Θij): Refers to the natural logarithm of the occurrence rate (Θij) of the event under study.The logarithmic transformation is common in statistical models to stabilize variability and ensure that values are positive.